On gravity and centrifugal settling of polydisperse suspensions forming compressible sediments

A mathematical model describing both the hindered settling and the consolidation of suspensions with particles of different sizes and densities forming compressible sediments is presented. The specific new element is a centrifugal configuration, which gives rise to a non-constant body force. Within a range of angular velocities, the model can be reduced to one (radial) space dimension. The result is a system of second-order strongly degenerate parabolic–hyperbolic convection–diffusion equations. For the special subcase of suspensions of rigid spheres, which do not form compressible sediments and for which the effective solid stress can be assumed to vanish, these equations form a first-order system of conservation laws. A type analysis shows that these equations include hyperbolic, hyperbolic–parabolic, and hyperbolic–elliptic systems, depending on the sizes and densities of the solid particles. A numerical high-resolution central difference scheme for the hyperbolic and hyperbolic–parabolic models is applied to solve the model numerically, and thereby to simulate centrifugation of two polydisperse suspensions.